Solve the following DE spring problem:
DE: 32 pound weight is attached to the lower end of a coiled spring suspended from the ceiling, spring constant being 3 pounds per foot. The weight is pushed upward by 5 feet and given downward velocity of 3 feet per second. The medium it is in offers a resistance in pounds numerically equal to 4 times the instantaneous velocity in feet per second.
1) determine the times when the weight will pass through equilibrium.
Note: I already found the equation of motion to be x(t)= -6e^(-t) + e^(-3t).
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